descartes

2012_01_19-text-th

When I was younger, among the branches of philosophy, I had studied a little logic and, among the subjects of mathematics, geometrical analysis and algebra, three arts or sciences which looked as if they ought to contribute something to my project. But in looking at them, I took care, because, so far as logic is concerned, its syllogisms and most of its other instructions serve to explain to others what one already knows or even, as in the art of Lully, to speak without judgment of things about which one […]

2012_01_19-text-th

Here are two passages from Shamos’s dissertation thesis, where he is looking at history of geometry from perspective of a computer scientist. Egyptian and Greek geometry were masterpieces of applied mathematics. It is well established that the original motivation for tackling geometric problems was the need to tax lands accurately and fairly and to erect buildings (Eves, 72). As often happens, the mathematics that developed has permanence and significance that far transcends Pharaoh’s original revenue problem. It is a field in which intuition abounds and new discoveries are within the […]

2012_01_19-text-th

…While it is true that every curve which can be described by a continuous motion should ve recognized in geometry, this does not mean that we should use at random the first one that we meet in the construction of a given problem. We should always choose with care the simplest curve that can be used in the solution of a problem, but it should be noted that the simplest means not merely the one most easily described, nor the one that leads to the easiest demonstration or construction of […]